From Accuracy to Robustness: A Study of Rule- and Model-based Verifiers in Mathematical Reasoning

arXiv:2505.22203 · cs.LG, cs.AI, cs.CL · Submitted 2025-05-28 · Read on arXiv

cs.LG, cs.AI, cs.CL

Submitted: 2025-05-28

Updated: 2026-08-27

Code: https://github.com/hkust-nlp/RL-Verifier-Robustness

Terminology

• Verifier — 298× in this paper · explained in 2 episodes
• Verification — 20× in this paper · explained in 2 episodes
• Reinforcement Learning — 18× in this paper · explained in 4 episodes
• Reward Hacking — 18× in this paper · explained in 8 episodes
• Accuracy — 17× in this paper · explained in 1 episode
• Benchmark — 13× in this paper · explained in 2 episodes
• Robustness — 12× in this paper · explained in 5 episodes
• Fine-Tuning — 7× in this paper · explained in 5 episodes
• Adam — 6× in this paper · explained in 2 episodes
• Consistency — 3× in this paper · explained in 3 episodes
• Core — 3× in this paper · explained in 2 episodes
• Adaptability — 2× in this paper · explained in 1 episode
• F1 Score — 2× in this paper · explained in 2 episodes
• Generalization — 2× in this paper · explained in 13 episodes
• Reinforcement Learning (RL) — 2× in this paper · explained in 24 episodes
• Ablation — 1× in this paper · explained in 1 episode
• Alignment — 1× in this paper · explained in 1 episode
• Chain-of-Thought (CoT) — 1× in this paper · explained in 4 episodes
• Communication Overhead — 1× in this paper · explained in 2 episodes
• GRPO — 1× in this paper · explained in 6 episodes
• Hybrid Approach — 1× in this paper · explained in 4 episodes
• Hybrid System — 1× in this paper · explained in 2 episodes
• Large Language Models (LLMs) — 1× in this paper · explained in 5 episodes
• Reasoning Traces — 1× in this paper · explained in 3 episodes
• Trace — 1× in this paper · explained in 2 episodes
• Verifiable Rewards — 1× in this paper · explained in 2 episodes

Sources

• L1: Controlling How Long A Reasoning Model Thinks With Reinforcement Learning
• Monitoring Reasoning Models for Misbehavior and the Risks of Promoting Obfuscation
• xVerify: Efficient Answer Verifier for Reasoning Model Evaluations
• Training Verifiers to Solve Math Word Problems
• DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning
• OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems
• Measuring Mathematical Problem Solving With the MATH Dataset
• Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model
• GPT-4o System Card
• OpenAI o1 System Card
• Tulu 3: Pushing Frontiers in Open Language Model Post-Training
• ProRL: Prolonged Reinforcement Learning Expands Reasoning Boundaries in Large Language Models
• Optimizing Test-Time Compute via Meta Reinforcement Fine-Tuning
• Seed1.5-Thinking: Advancing Superb Reasoning Models with Reinforcement Learning
• DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models
• HybridFlow: A Flexible and Efficient RLHF Framework
• Crossing the Reward Bridge: Expanding RL with Verifiable Rewards Across Diverse Domains
• Kimi k1.5: Scaling Reinforcement Learning with LLMs
• Qwen2.5 Technical Report
• Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement

Related papers

• Polynomial-Augmented Neural Networks (PANNs) with Weak Orthogonality Constraints for Enhanced Function and PDE Approximation
• AIRL-S: Unifying Reinforcement Learning and Search-Based Test-Time Scaling via Adversarial Inverse Reinforcement Learning
• Transformers as Bayesian In-Context Experimenters: Smoothness-Adaptive Efficient ATE Estimation
• Convergence issues in Relational Concept Analysis based on AOC-posets
• Beliefs Beyond Posteriors: Local-Consistency Optimisation for Bayesian Neural Networks
• Understanding Diffusion Models via Ratio-Based Function Approximation with SignReLU Networks